No, DR only stacks if it specifically says it does. The Barb, DD, and Armor spec do NOT mention stacking so they don't. Epic DR increases are meant to stack and so they stack with *every* type of natural (feat/class based) that you have.
So if a character had the following:
Barb for DR 1/-
Anointed Knight for DR 3/-
Armor Specialization for DR 2/-
Adamantine Armor for DR 2/-
Their effective DR would be 3/- as that is the highest source available (since none of them stack together).
If you had the first feat of Epic DR (3/- that stacks) your DR's would become:
Barb for DR 4/- (class/feat, so increased)
Anointed Knight for DR 6/- (class/feat, so increased)
Armor Specialization for DR 5/- (skill/feat, so increased)
Adamantine Armor for DR 2/- (item based, no increase)
All except Adamantine Armor are permanent sources of DR so get the epic stacking benefit. If you took a second rank of Epic Damage Reduction you would gain 6/- stacked on those permanent abilities thus:
Barb for DR 7/- (class/feat, so increased)
Anointed Knight for DR 9/- (class/feat, so increased)
Armor Specialization for DR 8/- (skill/feat, so increased)
Adamantine Armor for DR 2/- (item based, no increase)
Logically they should stack (tough skin + magic oil over skin = super tough, protected skin) but the rules say they shouldn't.
http://www.d20srd.org/srd/specialAbilities.htm#damageReduction
http://www.d20srd.org/srd/epic/feats.htm#damageReduction